2016/04/21 by Volodymyr Mykhaylyuk, Mykhaylyuk, V.
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1604.06178
openalex publication_date 2016/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a characterization of countable discrete subspace A of a topological space X such that there exists a (linear) continuous mapping φ:Cp^*(A)→ Cp(X) with φ(y)|A=y for every y∈ Cp^*(A). Using this characterization we answer two questions of A.~Arhangel'skii. Moreover, we introduce the notion of well-covered subset of a topological space and prove that for well-covered functionally closed subset A of a topological space X there exists a linear continuous mapping φ:Cp(A)→ Cp(X) with φ(y)|A=y for every y∈ Cp(A).